The election of Egypt’s first Islamist president poses a challenge for the Obama administration, which is grappling with the reality of embracing a leader whose worldview often has been at odds with Washington.

“The [Obama] administration continues to feel out the Brotherhood rather than laying out a clear set of specifications regarding the Brotherhood’s cooperation on key American interests.”

Marina Ottaway, a senior associate in the Middle East program at the Carnegie Endowment for International Peace, said the administration has adopted a “wait-and-see” approach before it rejiggers its Egypt policy.

Lack of authority

Mr. Morsi will assume a post that has been largely stripped of authority by the Supreme Council of the Armed Forces, a military body that has been ruling Egypt since longtime President Hosni Mubarak was forced to step down last year. The new president is likely to spend much of his time in office locked in a power struggle with the military.

The military council has said that it will hand over executive powers to Mr. Morsi at the end of this month, but that it will retain legislative powers until a new constitution is drafted and a new parliament elected.

Earlier this month, Egypt’s top court ruled that the Islamist-dominated parliament must be dissolved because a third of its members had been elected illegally.

The Obama administration is still counting on the Egyptian military to secure U.S. interests, said Michele Dunne, director of the Atlantic Council’s Rafik Hariri Center for the Middle East.

“I think there should be a recalibration of the relationship, but I am not sure that the U.S. administration is really embarked on changing the relationship,” Ms. Dunne said.

Mubarak, who ruled Egypt for three decades, was a reliable U.S. ally in the Middle East, maintaining a peace agreement with Israel and strengthening a military-to-military relationship with the United States.

With Mr. Morsi at the helm, “Egypt will be a far less reliable partner and a frequent source of headaches,” Mr. Trager said.

The U.S.-Egyptian relationship will be more complex for the simple reason that the administration in Washington is no longer dealing with one man in Cairo, said Khairi Abaza, a senior fellow at the Foundation for Defense of Democracies in Washington.

“The U.S. will have to nurture relations with various political actors and negotiate its interests,” he said. “The relationship might become a little more complex, but it can become a much healthier one.”

Foreign policy vs. economic policy

The Morsi administration’s commitment to the 1979 Egyptian-Israeli peace treaty is the biggest unknown in the new relationship.

Mubarak received $1.3 billion in U.S. aid annually for keeping the peace with Israel. Brotherhood leaders have said they want to amend the treaty.

“Morsi will be looking for a more robust economic relationship, and perhaps a relationship that contains more strategic dialogue on economic as well as political issues, and less a relationship that is simply delivery of a lot of military aid in exchange for a certain set of military and security cooperation,” Ms. Dunne said.

Mr. Morsi, in his first televised speech as president-elect, sought to allay concerns in the U.S. and Israel by declaring his intention to preserve all of Egypt’s international accords.

Secretary of State Hillary Rodham Clinton this week described such statements as positive, but added, “We’ll have to wait and judge by what is actually done.”

Some analysts view the president-elect’s comments with skepticism.

“The U.S. is not as certain as it was in the case of Mubarak that the Muslim Brotherhood will respect the peace treaty,” Ms. Ottaway said.

Mr. Trager said: “Morsi has said that he will abide by all agreements, but has frequently carved out exceptions for popular will and strategic priorities, and the consensus in Egypt is that peace with Israel is not a strategic priority.”

Peace with Israel hinges on stability in the Sinai Peninsula, where a flare-up could set the region ablaze.

The Brotherhood’s support for closer ties with Iran also has set off alarm bells in Washington.

Mr. Morsi, however, is unlikely to come to office with a big foreign policy agenda, largely out of necessity, analysts say.

One of his biggest challenges will be to put the country’s economy back on track.

Egypt’s tourism industry, its main source of income, has been ravaged since the start of the anti-Mubarak uprising in January 2011.

These harsh economic realities likely will force the Brotherhood to moderate its foreign policy agenda.

“The Brotherhood is going to cultivate the support of the United States and Europe because they need foreign investment and improved trade arrangements,” Ms. Dunne said.

Mr. Abaza agreed.

“Egypt needs the U.S. for the sake of its economy and for Washington’s support in financial institutions such as the World Bank and the [International Monetary Fund],” he said.